Such a train radio system and such a mobile station are known from DE 42 22 237 A1. The respective train radio system is described as a cellular radio system for a train radio, wherein adjacent radio stations use different radio frequencies, so that a number of radio cells are aligned in the form of a radio-cell chain along the route. The therein described mobile station inside the vehicle (train) is connected to that radio station in whose radio cell it is located. As described in DE 42 22 237 A2, to realize the train radio system in a simple manner, it is designed in accordance with the "GSM" (Global System for Mobile Communications) standard. A control device, which is connected to the radio stations, controls the establishment of a radio link from one radio cell to another while the train is traveling. However, in principle, handover within a cellular radio network requires a costly network structure. In this way for example, the GSM network requires radio switching stations with so-called home data banks and visitor data banks to check in the mobile station when establishing a radio link, and to determine the present and the next radio cell ("serving cell" and "target cell") when handing over the radio link. In addition, the known train radio system, whose network structure corresponds to the GSM standard, is unable to safeguard the radio transmission by simultaneously establishing two or more radio links between the mobile station and different radio stations.